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Sharper uncertainty principles for the windowed Fourier transform
Liu M.-S.3; Kou K.I.1; Morais J.4; Dang P.2
2015-01-02
Source PublicationJournal of Modern Optics
ISSN13623044 09500340
Volume62Issue:1Pages:46-55
Abstract

The windowed Fourier transform replaces the Fourier transforms sinusoidal wave by the product of a sinusoid and a window which is localized in time. It has been shown to represent a powerful tool for non-stationary signals and time-varying systems. In the present paper, we investigate the uncertainty principles in the short-time spectral domain. Two sharper uncertainty principles for complex signals are proposed. The tighter lower bounds are related to the covariance of time and frequency, and can be achieved by complex chirp signals with Gaussian envelope. The results presented in this paper explain interesting phenomena in signal recovery problems where there is an interplay of missing data and is time-limiting.

KeywordAmplitude-phase Representation Of Signal Hardy-sobolev Space Heisenberg's Uncertainty Principle Instantaneous Frequency Signal Moment Windowed Fourier Transform
DOI10.1080/09500340.2014.952692
URLView the original
Indexed BySCI
Language英语
WOS Research AreaOptics
WOS SubjectOptics
WOS IDWOS:000346504500007
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Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.Macau University of Science and Technology
3.South China Normal University
4.Universidade de Aveiro
Recommended Citation
GB/T 7714
Liu M.-S.,Kou K.I.,Morais J.,et al. Sharper uncertainty principles for the windowed Fourier transform[J]. Journal of Modern Optics,2015,62(1):46-55.
APA Liu M.-S.,Kou K.I.,Morais J.,&Dang P..(2015).Sharper uncertainty principles for the windowed Fourier transform.Journal of Modern Optics,62(1),46-55.
MLA Liu M.-S.,et al."Sharper uncertainty principles for the windowed Fourier transform".Journal of Modern Optics 62.1(2015):46-55.
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